Best base town Amalfi Coat

5 days is not. Too much. However i would choose to stay in Sorrento. The best base, with access to ferries,and or bus to the towns u list.

I second the vote for Sorrento, as it's better for transportation (rail and bus links) and has a good selection of hotels and restaurants. Positano has no rail links, so not nearly as convenient. Which town to use as a base will depend to some extent on where you want to tour in that area.

If you are planning days to see ...
1. Capri
2. Positano
3. Amalfi & Ravello
4. Pompeii & Herculaneum
5. Naples
...then Sorrento, as advised, is your best choice for ease of logistics.

Another vote for Sorrento, which technically isn't the Amalfi Coast but on the edge of it. The most varied amount of public transport options around the region are available from there.

Regarding your 2nd posted question about getting around in April:

Capri: high-speed ferry
Positano: SITA bus or (except for high-sea days) high-speed ferry
Amalfi: SITA bus or high-speed ferry
Ravello: SITA bus from Amalfi
Pompeii - train from Sorrento
Naples - train to/from Sorrento

I recommend a couple nights in Sorrento and the rest on the Amalfi coast if you plan on seeing Pompeii/Herculaneum/Naples. I would not want to treat the coast as a series of day trips from and back to Sorrento every day. It's a lot of wasted time. Also, day tripping into Amalfi and the up to Ravello is difficult, and I consider Ravello a highlight.

My vote for a stay on the Amalfi coast is Atrani, a small town just a 10min (flat) walk from Amalfi. There's good Airbnb options along with a hotel or two. It's quaint, local-feeling, has its own sandy beach and has some excellent restaurants. You get all the convenience of Amalfi's superior transportation connections without having to stay in Amalfi (which I felt was kind of an overrun dump). Ravello is very easy from here. If not there, then probably Positano, which is scenic beyond words and is basically what you imagine the place to be.

True. With 5 nights, it would be possible to divide them among two places.

This last March we based in Sorrento for 5 nights, and from a logistics standpoint were happy we did. We felt confident taking relatively exhausting day trips to Naples and Positano that we'd have a place to return in late afternoon to nap, then find a top-notch, inexpensive trattoria at which to walk to and dine. For that alone it's worth my vote.

But...we passed a couple spots that I would love to try out. First, not far from Sorrento is Vico Equense, which we saw on the way to the Naples airport. As gorgeous and beautiful as anything on the other side of the peninsula. On the A.C. we stopped for a few minutes in Maiori, which had a wonderful little park between the shore road and the cliff to the sea that was simply breathtaking. Observed a little playground where small children were having fun, and I wanted to run up to them and say, 'do you realize how fantastic this is?!' Another insane American...

As much as I enjoy having only one place to hang my hat, on my next trip to the peninsula, if it's more than 3 days I'll split it up between Sorrento and one of those two venues.

5 nights is good / ideal for the area. You should in the future state nights not days, you may actually only mean 4 nights by 5 days. 4 nights for the area I feel is the minimum.
I would choose Positano. just so you understand the scale of the area none of your 3 options listed are cities, each are very small towns.

I have stayed in both Sorrento and Positano and agree Sorrento is better logistically than anywhere else.
Sorrento is much larger than the other towns you have listed, if you want to see everything on djp-syd's list Sorrento makes more sense.
I just preferred Positano by a fairly large margin and when we return to the area will stay again in Positano but would not again stay in Sorrento.

The time of year would matter some though, if off season Sorrento would be the only place with a ferry running to Capri for example where the rest of the year it wouldn't matter much if you visited Capri from Sorrento or Positano.

Amalfi the town did not really impress me.

Ravello did impress me a good deal but is so small and kind of isolated that I don't think it makes a good base option. For your second trip another year Ravello may be a good option.